Moving executables around between different Linux distributions is notoriously difficult. If you want to make sure a binary built on your desktop will work on the netbooks you have to either ensure that all the libraries you use are present on the netbooks in a version compatible to that you link against on your desktop. As this is unlikely to be the case, you should either copy ship these libraries along the executable or use static linking.

Assuming you already have the required compiler and libraries on the netbooks but cannot afford the overhead of installing the whole Qt SDK just to use qmake there are two options :
  • switch to another build system (e.g. CMake) which can be installed standalone, contrary to qmake
  • copy the qmake binary (same remark about libs but I think qmake doesn't have too many dependencies) and the content of /usr/share/qt/mkspecs (or wherever the mkspecs are stored on your desktop) to the netbooks